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# What exactly does 44.1 kHz sampling mean in for sound recording and reproduction? (1 Viewer)

#### Chris PC

Senior HTF Member
Here is a question I posted at AVS that I thought of while discussing records and CD's.

What exactly does it mean that a CD is sampled at 44.1 kHz? Does that mean that a 10,000 hz sinewave only has 4 samples per wavelength? I know this is wrong, because then it would sound like crappola. So what does it really mean that sampling is done at 44.1 kHz and what is the resolution of the sampling if it is more than the 44.1 kHz figure what else is involved???

#### Justin B

##### Agent
With redbook CD's, the continuous analogue sound waves are divided into discrete samples. A sampling rate of 44.1 kHz means that 44,100 samples are taken every second. The 'resolution' of the sampling is 16 bit, which means that every discrete sample is represented by a 16 bit binary number. The sampling rate is independent of the frequency of the sound that is being sampled.

#### Mark Romero

##### Second Unit
My understanding is as follows so don't jump down my throat if I am wrong:

A 1KHz sine wave sampled at 8Khz would in fact be sampled 8 times. A 1Khz sine wave sampled at 44.1KHz would be sampled 44.1 times. The "samples" of the sine wave, if you drew it on a piece of paper, would form a sort of square wave and thus giving you a digital signal once some filtering and other stuff is done. A 10KHz signal would be sampled 4 times. That would be all that is needed for an accurate representation of a signal at that frequency. I don't recall off the top of my head the range of human hearing.

#### Craig F

##### Second Unit
What exactly does it mean that a CD is sampled at 44.1 kHz? Does that mean that a 10,000 hz sinewave only has 4 samples per wavelength? I know this is wrong, because then it would sound like crappola.
You only need 2 samples per cycle to represent a sinewave. One for the high peak and one for the low peak. This is where the 2X sample rate to represent a frequency comes from. The filters on the output of the DACs smooth these samples to try and recreate the original waveform. Upsampling can make the job of the filters easier by mathmatically interpolating addtional points in between the real samples.

#### Bob McElfresh

Senior HTF Member
Search the web for "Nyquest". A scientist basically said that to completly capture something that varies with time, you must sample at twice it's highest frequency.
Human hearing goes up to about 20,000 hz.
So we have to sample at a frequency of 40,000 hz.
But sounds do go beyond 20,000 hz and tests showed that if you sampled at 40,000 hz, it became audible. So they added a bit and chose 44.1 khz as a sampling rate for the CD spec.
4 samples per wavelength.. Yep. You've been listening to it for years.
But now you see why there is such interest in the 96 Khz Super Audio and DVD Audio formats. People start to do the math and say ... wait a minute!

#### KeithH

Senior HTF Member
Bob said:

But now you see why there is such interest in the 96 Khz Super Audio and DVD Audio formats.
The sampling rate for SACD is 2.8224 MHz. Also, the DVD-Audio specification allows for sampling up to 192 kHz.

Given Nyquist's theory of sampling at twice the highest frequency of interest, is this why 8x is often called oversampling? If 2x is required, does 8x oversampling mean that the number of samples is 16x times the highest frequency? Is oversampling completely different? Regardless of the oversampling performed by a CD player, CD is still 44.1 kHz (without considering upsampling).

#### Chris PC

Senior HTF Member
Wow. Pretty interesting. You see what I mean though? When i first heard about CD technology and how it worked, I thought, 44.1 kHz? Wow, thats high enough resolution. It was only a few weeks ago after I started playing with sound again that I thought, "wait a minute", a 10,000 Hz sound would only have 4 samples. Thats hardly high resolution. I guess I sort of understand the filtering and shaping of the waveform, but it is still weird.
For instance, a 10,000 Hz sound wave would have 4 samples, each with a value that corresponds somehow with the resolution of 16 bit CD's, 65,000 levels, right? There is probably so much more than that. Thanks for the search hints. I guess I'd better start researching and reading

#### Craig F

##### Second Unit
Keith,

Oversampling and upsampling are basically the same thing. They interpolate the data to create a artificially higher sample rate. This allows for gentler output filters which results in less noise and distortion. My understanding of the difference is that oversampling happens within the DAC. Upsampling happens before the DAC and is not limited to integer scaling. e.g. 44.1kHz to 96kHz.

#### KeithH

Senior HTF Member
Craig, thanks for the information. That makes sense since one cannot turn off oversampling, but some players allow one to turn off upsampling. I always had an idea that oversampling was related to upsampling, but I never asked and never saw it discussed. Thanks again for chiming in here.

I have limited experience with upsampling players or upsampling outboard DACs, but I imagine upsampling is preferred over oversampling. My assumption is based on the fact that many budget players oversample, but only high-end players upsample. Unless it is all smoke and mirrors, I assume upsampling is more advanced than is oversampling. Regarding the smoke and mirrors point of view, I have read comments on Audio Asylum from people who prefer to have the upsampling mode turned off on certain players. Furthermore, I have read comments from people who prefer 24/96 upsampling to 24/192. I am not about to say that upsampling is smoke and mirrors, but it does not appear to be universally accepted.

One other fundamental question I have is if oversampling is universally applied in CD players. In other words, without considering players that upsample, do all players oversample? Are there players that simply process at 44.1 kHz? I imagine there are, but frankly, I have not paid much attention to this spec. in CD players. I know that oversampling goes back many years, so I was thinking that it is commonly employed nowadays.

#### Rob Roth

##### Stunt Coordinator
Oversampling is no panacea. Basically the DACD grinds the same, limited data for addt'l passes to better represent the original sounds on its output. You still need improved filters to take advantage of the slightly revised signal. BTW, there are definite declining marginal returns here, no magic or free lunch. 16x oversampling WILL NOT give twice the quality of 8x oversampling. Also, the more that is done in the DAC (multiple operations) the more potential for noise and artifacts.

Upsampling is similar but better, the limited data set is augmented prior to the D to A conversion. This can result in improved quality assuming the downstream electronics are also improved.

These techniques, while clever, are still limited by the incoming data. It's a bit like using Hamburger Helper...

#### Chris PC

Senior HTF Member
Two samples to replicate a 20,000 hz signal. weird.

#### Rob Roth

##### Stunt Coordinator
It's not completely weird. The trick is to know (assume) that the signal which you are trying to replicate is a sinewave. If you assume that, and build your circuit so that it 'makes' sinewaves, then you only have to input 2 bits of information, the positive peak and the negative. From that the digital electronics will 'know' to make a sinewave of 'x' frequency.

The real issue is the beating of frequencies. If you combine a pure 1k sinewave and a pure 3k sinwave you will produce, along with the source tones, a difference tone (3k-1k=2k). This 2k tone will now join the source tones. This is a very good thing for live music because it allows instruments playing together to produce a staggering spectrum of sounds. It is a very bad thing in digital electronics. Say you use your 44k sampling frequency to provide the bits to specify a 20k signal. You also produce a 44k-20k=24k tone. This is probably undesireable. So the simle answer is a "brickwall" filter that blocks all frequencies above 20k. For various reasons, filters that try to suddenly attenuate all higher frequencies by, say, 80-100 dB, are problematic.

Notice that the simple math of difference tones allows you to reproduce tones BELOW the cutoff frequency; e.g. 44k-4k=40k, and 40k is safely above the cutoff frequency of the brickwall filter.

By oversampling you can 'sample higher', but to get the benefit you must also improve the filters so that they attenuate more gradually and avoid some of the problems any filter introduces in a circuit.

This is very simplified ( you might ask why 44.1k?) but it gives some idea. The important think to remember in digital electronics is that world length (16 bits vs. 24) specifies how precisely you can replicate amplitude changes, and sampling frequency (44.1k vs. 96k)determines what frequencies you can replicate. With frequency and amplitude info digital can 'approximate' the original analog waveforms.

#### Mark Romero

##### Second Unit
I guess I still remember the digital theory I learned 20 years ago. Amazing.

#### KeithH

Senior HTF Member
Larry,
Rob,
I agree with you about the limitations of the data and format. Oversampling and upsampling can only do so much.
You said:
These techniques, while clever, are still limited by the incoming data. It's a bit like using Hamburger Helper...
I've always preferred Tuna Helper myself.

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